Asked by Tsgh
Zwena chose to revise her model to better fit the data from 1820 to 1900.
q(x) = 1904(1.0611)^x
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That model is an exponential growth model. Interpreting x as years since 1820 (so x = 0 corresponds to 1820):
- q(x) = 1904(1.0611)^x means the quantity starts at q(0) = 1904 and grows by a factor 1.0611 each year (an annual growth rate of 6.11%).
- Natural (continuous) growth rate r = ln(1.0611) ≈ 0.0593 ≈ 5.93% per year.
- Doubling time ≈ ln 2 / ln(1.0611) ≈ 0.6931 / 0.0593 ≈ 11.7 years.
- Reasonable domain for the fit is 0 ≤ x ≤ 80 (1820 through 1900).
Example values:
- q(1) ≈ 1904(1.0611) ≈ 2020.3
- q(80) ≈ 1904(1.0611)^80 ≈ 2.19 × 10^5 (about 219,000)
Do you want me to evaluate q(x) for particular years, plot the curve, or compare this to the original model?
- q(x) = 1904(1.0611)^x means the quantity starts at q(0) = 1904 and grows by a factor 1.0611 each year (an annual growth rate of 6.11%).
- Natural (continuous) growth rate r = ln(1.0611) ≈ 0.0593 ≈ 5.93% per year.
- Doubling time ≈ ln 2 / ln(1.0611) ≈ 0.6931 / 0.0593 ≈ 11.7 years.
- Reasonable domain for the fit is 0 ≤ x ≤ 80 (1820 through 1900).
Example values:
- q(1) ≈ 1904(1.0611) ≈ 2020.3
- q(80) ≈ 1904(1.0611)^80 ≈ 2.19 × 10^5 (about 219,000)
Do you want me to evaluate q(x) for particular years, plot the curve, or compare this to the original model?
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